常曲率空间中平均曲率为常数的迷向子流形

Isotropic Submanifolds with Constant Mean Curvature in the Space with Constant Curvature

设M~α是n维黎曼流形,S^(n+p)(C)是(n+p)维截面曲率为常数C的黎曼流形,设f:M^n(?)S^(n+p)(C)是具有常中曲率H的迷向浸入,设K和R分别是M^n的截面曲率的下确界和数量曲率。本文给出K和R满足一定的关系,从而得到这种子流形是全脐子流形的几个充分条件。

Let S^(n+p)(c)be an(n+p)—space with constant Curvature C, and M^n a connected Riemannian manifold of dimension no Let f: M^n(?)S^(n+p)(c) be an isotropic immersion with constant mean curvature H. Let K and R be the infimum of sectional curvature and the scalar curvature of M^n, respectively. In this paper we gived some relation of K and R, and we obtained this submanifold is totally umbilical submanifolds.